Secret Ballot Protection Act of 2007 - Amends the National Labor Relations Act to make it an unfair labor practice for: (1) an employer to recognize or bargain collectively with a labor organization that has not been selected by a majority of the employees in a secret ballot election conducted by the National Labor Relations Board; and (2) a labor organization to cause or attempt to cause an employer to recognize or bargain collectively with a representative that has not been selected in such manner.